Meta learning algorithms for few-shot video recognition use complex, episodic training but they often fail to learn effective feature representations. In contrast, we propose a new and simpler few-shot video recognition method that does not use meta-learning, but its performance compares well with the best meta-learning proposals. Our new few-shot video classification pipeline consists of two distinct phases. In the pre-training phase, we learn a good video feature extraction network that generates a feature vector for each video. After a sparse sampling strategy selects frames from the video, we generate a video feature vector from the sampled frames. Our proposed video feature extractor network, which consists of an image feature extraction network followed by a new transformer encoder, is trained end-to-end by including a classifier head that uses cosine similarity layer instead of the traditional linear layer to classify a corpus of labeled video examples. Unlike prior work in meta learning, we do not use episodic training to learn the image feature vector. Also, unlike prior work that averages frame-level feature vectors into a single video feature vector, we combine individual frame-level feature vectors by using a new Transformer encoder that explicitly captures the key, temporal properties in the sequence of sampled frames. End-to-end training of the video feature extractor ensures that the proposed Transformer encoder captures important temporal properties in the video, while the cosine similarity layer explicitly reduces the intra-class variance of videos that belong to the same class. Next, in the few-shot adaptation phase, we use the learned video feature extractor to train a new video classifier by using the few available examples from novel classes. Results on SSV2-100 and Kinetics-100 benchmarks show that our proposed few-shot video classifier outperforms the meta-learning-based methods and achieves the best state-of-the-art accuracy. We also show that our method can easily discern between actions and their inverse (for example, picking something up vs. putting something down), while prior art, which averages image feature vectors, is unable to do so.